In clinical radiotherapy, the choice of the fractionation parameters: total time, number of fractions, dose per fraction, time-spacing of the fractions, is still largely based on experience. The present project develops a formalism to describe the normal tissue reactions to irradiation regimens over time in terms of the (indirect) reactions of the functions of normal tissue in relation to the reaction to radiation damage to the stem cells or transition cells. Normally there is a steady state of regular replacement of the normal attrition of functioning cells. This equilibrium condition is upset by radiation lethal damage to sensitive stem cells and transition cells. Full or tolerable recovery of functionality depends on the level of damage to the stem cell population, the distribution of damage over time, and on the tissue kinetic characteristics. Similar considerations apply to the tumor. The present model uses either the Linear-Quadratic or the Two-Component model for the immediate survival of vulnerable normal tissue or clonogenic tumor cells. It requires selection of tissue characteristics such as overall normal tissue turn-over time, acute stem cell doubling time, sublethal damage recovery time, and tolerance level functionality, in order to computer- generate time-dose response curves consistent with actual clinical response patterns, observed with conventional regimens. For tumors, similar selections are needed, as well as a criterion for cure rate. Successful selections are then tested with known alternative schemes. The ultimate aim is to develop reliable predictive rules for clinical radiation therapy.